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Spectral Representation of Deterministic Signals: Fourier Series and Transforms

In: A First Course in Statistics for Signal Analysis

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  • Wojbor A. Woyczyński

    (Case Western Reserve University, Department of Statistics and Center for Stochastic and Chaotic Processes in Sciences and Technology)

Abstract

In this chapter we will take a closer look at the spectral, or frequency-domain, representation of deterministic (nonrandom) signals which was already mentioned in Chap. 1. The tools introduced below, usually called Fourier, or harmonic, analysis will play a fundamental role later in our study of random signals. Almost all of the calculations will be conducted in the complex form. Compared with working in the real domain, the manipulation of formulas written in the complex form turns out to be simpler and all the tedium of remembering various trigonometric formulas is avoided. All of the results written in the complex form can be translated quickly into results for real trigonometric series expressed in terms of sines and cosines via the familiar de Moivre’s formula from Chap. 1, e jt = cos t = j sin t.

Suggested Citation

  • Wojbor A. Woyczyński, 2011. "Spectral Representation of Deterministic Signals: Fourier Series and Transforms," Springer Books, in: A First Course in Statistics for Signal Analysis, chapter 0, pages 21-49, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8101-2_2
    DOI: 10.1007/978-0-8176-8101-2_2
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